Amplifiers are used in many environments and are one of the most widely used electronic devices. Typical amplifiers receive a differential voltage and have a single output. Fully differential amplifiers may receive a differential voltage and have a differential output. Typically the output of the amplifier is controlled either by negative feedback, which largely determines the magnitude the voltage gain, or by positive feedback, which facilitates regenerative gain and oscillation (i.e., it attempts to keep the input constant).
FIG. 1 illustrates a front end of a fully differential amplifier 100. The amplifier may include a first transistor 101 receiving a first input voltage Vip at a positive input terminal and a second transistor 102 receiving a second input voltage Vin at a negative input terminal of the amplifier 100. The output Iout of the amplifier 100 is the difference in current between the collectors of transistors 101 and 102 (i.e., Ip−In). The output Iout is based upon the input voltages Vip and Vin and the tail current Itail present at the emitters of transistors 101 and 102. The tail current is controlled by current mirror 103. The current mirror may include a first transistor 104, controlled by a fixed current source 106, and a second transistor 105, which provides the tail current Itail to the differential transistors 101 and 102. The current mirror attempts to match the current passing through transistor 104 into transistor 105. Accordingly Itail will be approximately equal to Ibias.
When there is a large differential input voltage (i.e., when the difference between the input to the positive terminal and the negative terminal of the amplifier is large), the output of the amplifier tends to become distorted because the transconductance Gm of the input transistors in the amplifier is non-linear. FIG. 1b illustrates the output current versus the differential input voltages for the amplifier illustrated in FIG. 1a. Ideally the output current would be linear over a large range of differential input voltages, as indicated in FIG. 1b. However, because of the non-linear output current behavior of the transistors in the amplifier, the actual current output from the amplifier becomes distorted. Transconductance is the derivative of ratio of the current at the output port and the voltage at the input ports (Gm=(ΔIout/ΔVinput) of the amplifier. For the amplifier illustrated in FIG. 1a, the transconductance can be calculated using equation 1.1:
                    Gm        =                              (                                                            α                  F                                ×                                  I                  tail                                                            2                ×                                  V                  T                                                      )                    ⁢                      (                          1              -                                                tanh                  2                                ⁡                                  (                                                                                    V                        ip                                            -                                              V                        in                                                                                    2                      ×                                              V                        T                                                                              )                                                      )                                              (        1.1        )            where αF is ratio of collector current to emitter current of transistors 101 and 102 and VT is the thermal voltage of transistors 101 and 102. Because of the distortion caused by the transconductance of the amplifier at large differential input voltages the output of the amplifier becomes distorted. As seen in FIG. 1c, the transconductance Gm of the amplifier is shaped like a bell curve. Accordingly, as the differential input voltage deviates from the operating point (i.e. zero), the output of the amplifier becomes distorted.